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DTSTART:20211107T020000
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DTSTART:20220313T020000
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UID:calendar.25539.field_event_date_2.0@math.wustl.edu
CREATED:20220311T214859Z
DESCRIPTION:Abstract: In his paper, Quantum Unsharpness and Symplectic Rig
idity, Leonid Polterovich talks about the importance of the “intrinsic no
ise operator”, a measurement which analyzes the probabilities of an obser
vable in a quantum system (mathematically, these observables are function
s in a vector space). Polterovich proves that the maximum value the intrin
sic noise operator can take is related to the “degree of non-commutativity
” of the observable. In my thesis, I analyze this degree for a simple spa
ce and treat operators as matrices, creating my own value called the “com
mutator indicator”. Finding the commutator indicator turns into the follow
ing problem: we are given n matrices A_1, A_2, . . . , A_n that sum up
to the identity matrix. We must take the matrix norm of the sum of the adj
acent pairwise commutators of these matrices, and the commutator indicato
r is the maximum possible value of this norm. In my paper, I present the
results for maximizing the commutator indicator for three 2x2 matrices, a
long with the concrete maximum value itself and a set of matrices that yie
ld this value. Then with the help of programming, I generalize to four 2x
2 matrices and make some conjectures for that case and cases beyond.\n\nHo
st: Xiang Tang
DTSTART;TZID=America/Chicago:20220329T110000
DTEND;TZID=America/Chicago:20220329T120000
LAST-MODIFIED:20220311T214859Z
SUMMARY:Senior Honors Thesis Presentation: 'On the Study of Commutator Indi
cators for Finite Matrices'
URL;TYPE=URI:https://math.wustl.edu/events/senior-honors-thesis-presentatio
n-study-commutator-indicators-finite-matrices
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